Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,15,2}

Atlas Canonical Name {2,6,15,2}*720

Overview

Group
SmallGroup(720,831)
Rank
5
Schläfli Type
{2,6,15,2}
Vertices, edges, …
2, 6, 45, 15, 2
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

9-fold

15-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47);;
s2 := ( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44);;
s3 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)(31,46)(32,45);;
s4 := (48,49);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(49)!(1,2);
s1 := Sym(49)!(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47);
s2 := Sym(49)!( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44);
s3 := Sym(49)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)(31,46)(32,45);
s4 := Sym(49)!(48,49);
poly := sub<Sym(49)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;